Simplify the following expression: $\dfrac{3y^4}{y^2}$ You can assume $y \neq 0$.
Answer: $ \dfrac{3y^4}{y^2} = \dfrac{3}{1} \cdot \dfrac{y^4}{y^2} $ To simplify $\frac{3}{1}$ , find the greatest common factor (GCD) of $3$ and $1$ $3 = 3$ $1 = $ $ \mbox{GCD}(3, 1) = = 1 $ $ \dfrac{3}{1} \cdot \dfrac{y^4}{y^2} = \dfrac{1 \cdot 3}{1 \cdot 1} \cdot \dfrac{y^4}{y^2} $ $\phantom{ \dfrac{3}{1} \cdot \dfrac{4}{2}} = 3 \cdot \dfrac{y^4}{y^2} $ $ \dfrac{y^4}{y^2} = \dfrac{y \cdot y \cdot y \cdot y}{y \cdot y} = y^2 $ $ 3 \cdot y^2 = 3y^2 $